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POSIX.1 says, in 5.6.3.2 (page 105, lines 766-768):
If the process has appropriate privileges, an implementation may indicate
success
for X_OK even if none of the execute file permission bits are set.
The corresponding assertion in IEEE Std 2003.1-1992 says:
24(C)If the implementation provides a method for
associating with a process the appropriate privilege to override the file
access control mechanism:
When the process has the appropriate privileges to override the file
access control mechanism,
then a call to access(path, amode) will succeed when amode is set to
X_OK and any of the execute bits
are set or when the file is a directory.
Is the assertion correct in making a distinction between directories and
other file types?
My reading of POSIX.1 and POSIX.1b is that no such distinction is made in
the description of access() and
no such distinction is required by descriptions of file access control or of
directories elsewhere in the
standards. I feel that the words "or when the file is a directory" should not
be in the assertion.

Interpretation Response
The standard clearly states the distinction between directory search
permission and execute
permission for other file types (see lines 432-438 of 2.3.2), and
conforming implementations
must conform to this.

Rationale for Interpretation
The sentence preceeding the one from POSIX.1 mentioned in the
interpretation requests
refers to
section 2.3.2. That section says (page 21, lines 432-438):
(1) If a process has the appropriate privilege:

(a) If read, write, or directory search
permission is requested, access is
granted.

(b) If execute permission is requested,
access is granted if execute permission
is granted to at least one user by the
file permission bits or by an alternative access control mechanism;
otherwise,
access is denied.

The assertion rephrases this behavior in terms of the symbolic constant
X_OK.
The same symbolic constant is used both for execute permission and
directory search
permission (see Table 2.8 on page 28), which may obscure the
correspondence between
the assertion and the standard.
For a process with appropriate privileges, a call to access(path, X_OK)
must succeed if path refers
to a directory, even if none of the execute/search permission bits are set
for the directory.
The call must also succeed if path refers to a file with any execute
permission bits set.
Implementations may vary in the case where path refers to a file and not a
directory and there are
no execute bits set.